61. Webster's Online Dictionary - The Rosetta Edition Translate this page KOBYLARCZYK KOBYLINSKI KOBYLSKI KOC KOCAB KOCZELA KOCZERA KOCAJ KOCZUR KOCZWARA kochkoch OIL, koch OT koch SNOWFLAKE koch, EDWARD I koch, helge von koch, ILSE http://www.websters-online-dictionary.org/browse/indexko.html

Webster's Online Dictionary The Rosetta Edition Home Browse Credits About Us English Non-English Philip M. Parker, INSEAD. K Ka Kb Kc ... Next English Browse a b c d e f g h i j k l m n o p q r s t u v w x y z A Aa Ab Ac ... Zz Non-English Browse Afrikaans Albanian Arabic Asturian ... Zulu google_alternate_ad_url = "http://www.websters-online-dictionary.org/js/googlead.asp?kw=english+definition"; google_ad_client = "pub-7500086874932040"; google_ad_width = 728; google_ad_height = 90; google_ad_format = "728x90_as"; google_color_border = "336699"; google_color_bg = "FFFFFF"; google_color_link = "0000FF"; google_color_url = "008000"; google_color_text = "000000"; Philip M. Parker, INSEAD.

62. What (Koch's Snowflake) The koch Curve was studied by helge von koch in 1904. When consideredin its snowflake form, (see below) the curve is infinitely http://www.shodor.org/interactivate/activities/koch/what.html

What is the Koch's Snowflake Activity? This activity allows the user to step through the generation of a fractal made from deforming a line by bending it. This activity allows the user to step through the generation of a fractal made from deforming a line by bending it. The Koch Curve was studied by Helge von Koch in 1904. When considered in its snowflake form, (see below) the curve is infinitely long but surrounds finite area. To build the original Koch curve, start with a line segment 1 unit long. (Iteration 0, or the initiator) Replace each line segment with the following generator: Note that we are really taking the original line segment and replacing it with four new segments, each 1/3 the length of the original. Repeat this process on all line segments. Stages 0, 1, and 2 are shown below. The limit curve of this process is the Koch curve. It has infinite length. Notice also that another feature that results from the iterative process is that of self-similarity, i.e., if we magnify or "zoom in on" part of the Koch curve, we see copies of itself. The idea of the Koch curve was extended to the Koch "Snowflake" by applying the same generator to all three sides of an equilateral triangle; below are the first 4 iterations.

63. Koch-Kurve - Wikipedia Translate this page koch-Kurve. aus Wikipedia, der freien Enzyklopädie. Die koch-Kurve ist eine vomschwedischen Mathematiker helge von koch erstmals 1904 vorgestellte Kurve. http://de.wikipedia.org/wiki/Koch-Kurve

Koch-Kurve aus Wikipedia, der freien Enzyklopädie Die Koch-Kurve ist eine vom schwedischen Mathematiker Helge von Koch erstmals vorgestellte Kurve . Es handelt sich bei ihr um eines der ersten formal beschriebenen fraktalen Objekte. Die Koch-Kurve ist auch als Kochsche Schneeflocke bekannt; letztere entsteht aus geeigneter Kombination dreier Koch-Kurven. Inhaltsverzeichnis showTocToggle("Anzeigen","Verbergen") 1 Konstruktion 1.1 Konstruktion Graphisch dargestellt 2 Eigenschaften 3 Kochsche Schneeflocke ... bearbeiten Konstruktion Man kann die Kurve anschaulich mittels eines iterativen Prozesses konstruieren. Zu Anfang ist ein Linienstück der Länge "1" gegeben. Die Iteration besteht nun darin, dass alle Linienstücke der Kurve in drei gleichlange Stücke unterteilt werden, auf dem jeweils mittleren Stück ein gleichseitiges Dreieck errichtet wird, und die Basis dieses Dreiecks (also das ursprüngliche Drittelstück) entfernt wird. Diese Iteration wird nun unendlich oft wiederholt. Als Endergebniss entsteht die Koch-Kurve. bearbeiten Konstruktion Graphisch dargestellt Anfangslinie: 1. Iteration:

64. Kalender Translate this page Niels Fabian helge von koch 54 Jahre, Mathematiker (22.09.2001) Inhaltsuchen oben *25 Jan 1870 Stockholm +11 Mrz 1924 Danderyd. http://www.info-kalender.de/kal/k000125.htm

S a m i n f o k a l e n d e r J a n Januar Februar April Mai ... (suchen) Marie-Paule Belle Inhalt suchen oben *25 Jan 1946 Dagmar Berghoff Inhalt suchen oben *25 Jan 1943 Berlin Roy Black Inhalt suchen oben *25 Jan 1943 +9 Okt 1991 Filme Robert Boyle Inhalt suchen oben *25 Jan 1627 +30 Dez 1691 London Robert Burns 37 Jahre, schott. Dichter Inhalt suchen oben *25 Jan 1759 +21 Jul 1796 Dumfries Anton Diel 61 Jahre, Bundestagsabge. (SPD) Inhalt suchen oben *25 Jan 1898 +6 Apr 1959 Bundestag Antonio Eanes Inhalt suchen oben *25 Jan 1935 Alcains John Arbuthnot Fisher Inhalt suchen oben *25 Jan 1841 +10 Jul 1920 London Petra Gerster Inhalt suchen oben *25 Jan 1955 Worms David Grossman Inhalt suchen oben *25 Jan 1954 Jerusalem Niels Fabian Helge von Koch Inhalt suchen oben *25 Jan 1870 +11 Mrz 1924 Danderyd Inhalt suchen oben *25 Jan 1958 Uerdingen Dean Jones Inhalt suchen oben *25 Jan 1931 Morgan City Alabama. Alicia Keys Inhalt suchen oben *25 Jan 1981 New York NY. 60 Jahre, Bundestagsabge. (CDU) Inhalt suchen oben *25 Jan 1943 Essen Bundestag Witold Lutoslawski Inhalt suchen oben *25 Jan 1913 +7 Feb 1994 Warschau Tim Montgomery Inhalt suchen oben *25 Jan 1975 Gaffney South Carolina.

65. Koch's Snowflake, Mandelbrot's Coastline, Alaska Science Forum In 1904, the Swedish mathematician helge von koch described an interestingcuriosity. He proposed a mental exercise that could be http://www.gi.alaska.edu/ScienceForum/ASF9/920.html

Alaska Science Forum April 5, 1989 Koch's Snowflake, Mandelbrot's Coastline Article #920 by Carla Helfferich This article is provided as a public service by the Geophysical Institute, University of Alaska Fairbanks, in cooperation with the UAF research community. Carla Helfferich is a science writer at the Institute. Journalists love numbers almost as much as scientists do, and probably for the same reason: if you can put an exact number on it, it must be real. That was never more clear than during the oil spill in Prince William Sound. Readers, listeners, and viewers were given numbers for everything from how many gallons are in a barrel of oil to the dollar value of the annual pink salmon catch. They were told how many sea otters lived near Naked Island and how many square miles of sea water lay under the oily scum. Yet in all the news of threatened coastline, rare indeed were statistics on the length of that coastline. At first, that doesn't seem logical. A coastline is obviously real, so it must be measurable in real numbers. Well, yes and no. Contemporary mathematics, with roots in the early part of this century, raises some doubts. In 1904, the Swedish mathematician Helge von Koch described an interesting curiosity. He proposed a mental exercise that could be partially carried out in visible form by anyone with pencil, paper, and patience.

66. Koch Curve Definition Meaning Information Explanation om©trique ©l©mentaire pour l ©tude de certaines questions de la th©oriedes courbes plane by the Swedish mathematician helge von koch 1. The http://www.free-definition.com/Koch-curve.html

A B C D ... Contact Beta 0.71 powered by: akademie.de PHP PostgreSQL Google News about your search term Koch curve The Koch curve is a mathematical curve , and one of the earliest fractal curves to have been described. It appeared in a paper entitled "Une m©thode g©om©trique ©l©mentaire pour l'©tude de certaines questions de la th©orie des courbes plane" by the Swedish mathematician Helge von Koch [1]. The better known Koch snowflake (or Koch star ) is the same as the curve, except it starts with an equilateral triangle (instead of a line segment ). Eric Haines has developed the sphereflake fractal , a three- dimensional version of the snowflake One can imagine that it was created by starting with a line segment, then recursively altering each line segment as follows: divide the line segment into three segments of equal length. draw an equilateral triangle that has the middle segment from step one as its base. remove the line segment that is the base of the triangle from step 2. After doing this once the result should be a shape similar to a cross section of a witch's hat. The Koch curve is the limit approached as the above steps are followed over and over again.

67. Analytically student/perezc/demo/vonkoch.html. Niels Fabian helge von koch http//wwwgroups.dcs.st-and.ac.uk/~history/Mathematicians/koch.html. http://jamesrahn.com/SRHS/analytically.htm

Analytically Initial Question Numerically Graphically Recall from the previous studies that the Koch Curve is changing at each stage. Remember we were studying two measurements: length of each piece of the segment, and total length of the Koch Curve. Stage Number Length of each segment piece Total Length of Curve Using the pattern developed in the Numerical study, we found that the length of each piece of the segment could be represented as a power of . So, for example, the length of each piece of the Koch Curve in stage 10 was What would the length of each piece of the Koch Curve be in the Nth stage? It would be reasonable to believe the length of each piece of the Koch Curve in the Nth stage to be What is happening to this length as N approaches larger numbers? From the numerical study, you can see that the fractional representations always have a 1 in the numerator and a larger number in the denominator as the Koch Curve moves through the various stages. This would mean that the length of the segment pieces would approach, but never equal zero. There would always be some measurement for the length. In mathematics we would describe this phenomena as the limit of , as N approaches infinity, to be equal to zero or Recall that we also studied the length of the Koch Curve as various stages. Recall that the length of the Koch Curve at Stage 10 was

68. 455-456 (Nordisk Familjebok / Uggleupplagan. 14. Kikarsikte - Kroman) Gottschee (se de). koch, Eoban. Se Hessus, HE - koch. 1. Nils Samuelvon - koch. 2. Richert Vogt von - koch. 3. Nils Fabian helge von. http://www.lysator.liu.se/runeberg/nfbn/0252.html

Nordisk familjebok Uggleupplagan. 14. Kikarsikte - Kroman (1911) Tema: Reference Table of Contents / Innehåll Project Runeberg Catalog ... Print (PDF) On this page / på denna sida - Koburger, A. Se Koberger - Koburg-Koháry. Se Koháry. - Kobza, instrument. Se Kobzar. - Kobzar - Koccidier. Se Bakteorologi, sp. 730 och Coccidiaria. - Koccidiös, som innehåller koccidier. - Koccinellor, zool. Se Nyckelpiga. - Koccygodyni - Kocevje, sloveniska namnet på Gottschee (se d. e.). - Koch, Eoban. Se Hessus, H. E. - Koch. 1. Nils Samuel von - Koch. 2. Richert Vogt von - Koch. 3. Nils Fabian Helge von Below is the raw OCR text from the above scanned image. Do you see an error? Proofread the page now! Här nedan syns maskintolkade texten från faksimilbilden ovan. Ser du något fel? Korrekturläs sidan nu! This page has never been proofread. / Denna sida har aldrig korrekturlästs. Project Runeberg, Sat May 15 18:57:33 2004 (aronsson) http://www.lysator.liu.se/runeberg/nfbn/0252.html

69. In Der Fassung Der Handschrift : Literaturkritik.de Translate this page von helge Schmid. Die Nachfahren Max Brods in der Betreuung von Kafkas Werk haben herausgegebenwerden (die Edition besorgten Hans-Gerd koch, Michael Müller http://www.literaturkritik.de/public/rezension.php?rez_id=5813&ausgabe=200303

70. Kromme Van Koch< Kromme van koch. In 1904 ondekte de Zweedse wiskundige helge von kocheen kromme, die heden ten dage bekend staat al de Kromme Van koch . http://studwww.ugent.be/~brminnae/maths/Koch.html

Kromme van Koch In 1904 ondekte de Zweedse wiskundige helge von Koch een kromme, die heden ten dage bekend staat al de Kromme Van Koch . Haar ontdekking was van grote aard: ze had een kromme ontdekt die in geen enkel punt afleidbaar (in 1872 had Weierstrass ook al zo'n dergelijke kromme ontdekt). Deze kromme behoort tot een grote familie: de familie van Koch. Bij de Kromme Van Koch vertrekt men van een lijnstuk, de basis genoemd. Die basis wordt dan verdeeld in 3 gelijke stukken, het middelste wordt weggelaten en vervangen door een gelijkzijdige driehoek zonder basis. Deze figuur noemt men de generator . De volgende stappen zijn nu steeds analoog. Men beschouwt elk lijnstuk als een nieuw basis en verdeelt die dan weer als voorheen. Dus: basis: generator: Na dit 'oneindig keer' gedaan te hebben, verkrijgen we Kromme Van Koch Devolgende applet illustreert de eerste 6 stappen. Nu doen we nog eens identiek hetzelfde, maar als basis nemen we nu een driehoek in plaats van een lijnstuk. Nu bekomen we het Eiland van Koch of de Sneeuwvlok van Koch Hieronder volgt een illustratie: We kunnen dit ook inwendig doen, dan bekomen we een soort gletsjer-eiland zoals hieronder aangegeven is.

71. NetLogo Models Library: Koch Curve instead. WHAT IS IT? helge von koch was a Swedish mathematician who,in 1904, introduced what is now called the koch curve. Here http://ccl.northwestern.edu/netlogo/models/KochCurve

Home Page Download Models Library Community Models User Manual: HTML Printable (PDF) FAQ Contact Us NetLogo Models Library: Sample Models/Mathematics/Fractals (back to the library) Koch Curve Run Koch Curve in your browser uses NetLogo 2.0.1 requires Java 1.4.1+ system requirements Note: If you download the NetLogo application, every model in the Models Library (besides the Community Models) is included. If you have trouble running this model in your browser, you may wish to download the application instead. WHAT IS IT? Helge von Koch was a Swedish mathematician who, in 1904, introduced what is now called the Koch curve. Here is a simple geometric construction of the Koch curve. Begin with a straight line. This initial object is also called the "initiator." Partition it into three equal parts. Then replace the middle third by an equilateral triangle and take away its base. This completes the basic construction step. A reduction of this figure, made of four parts, will be used in the following stages. It is called the "generator." Thus, we now repeat, taking each of the resulting line segments and partitioning them into three equal parts, and so on. The figure below illustrates this iterative process. Step 0: "Initiator"

72. Text4 In the early 1900s, the Swedish mathematician helge von koch constructedan object made up of a sequence of identical steps. He http://www.scientific-religious.com/text4.html

IV. The Principle of Self-Similarity Euclidean geometry is the science that deals with regular one-dimensional lines, two-dimensional planes and three-dimensional solids. Nevertheless, about the same time the theory of self-organization was being developed but independently of it, the French mathematician Benoit Mandelbrot formulated a geometry that portrays the irregular shapes of clouds, mountains, coastlines, leaves, flowers, trees, and the countless other irregular shapes found in Nature. He named it fractal geometry. (The word fractal comes from the Latin "fractus" which means "broken." Fractus is also at the core of the words "fracture" and "fraction".) An example of an artificial fractal is the Koch curve. In the early 1900s, the Swedish mathematician Helge von Koch constructed an object made up of a sequence of identical steps. He started with an equilateral triangle. On each side he added equilateral triangles with sides half the size of the original, making a Star of David. The operation was repeated which led to a shape similar to a snowflake.

73. Biography-center - Letter V von koch, helge wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/koch.html;von Leibniz, Gottfried www-history.mcs.st-and.ac.uk/~history/Mathematicians http://www.biography-center.com/v.html

Visit a random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish V 205 biographies Vaca, Alva Nuñez Cabeza de www.pbs.org/weta/thewest/people/a_c/cabezadevaca.htm Vaca, Alva Nuñez Cabeza de www.newadvent.org/cathen/03126c.htm Vacca, Giovanni www-history.mcs.st-and.ac.uk/~history/Mathematicians/Vacca.html Vaga, Perino del www.getty.edu/art/collections/bio/a952-1.html Vailati, Giovanni www-history.mcs.st-and.ac.uk/~history/Mathematicians/Vailati.html Val, Patrick du www-history.mcs.st-and.ac.uk/~history/Mathematicians/Du_Val.html Vala, Katri www.kirjasto.sci.fi/kvala.htm VALEJO, Christiane www.christiane-valejo.com/Biography.htm Valentin, www.kirjasto.sci.fi/valentin.htm Valentin, Moise www.kfki.hu/~arthp/bio/v/valentin/biograph.html Valentine, www.knight.org/advent/cathen/15254b.htm Valerio, Luca

74. Koch S Curve efficient implementation. koch s Curve. An example of a simple fractalimage is koch s curve, named after Swedish helge von koch. The idea http://www.cs.auc.dk/~normark/eciu-recursion/html/recit-note-koch.html

75. What (Koch's Snowflake) The koch Curve was studied by helge von koch in 1904. When considered in its snowflakeform (see below) the curve is infinitely long but surrounds finite area. http://www.ecu.edu/si/cd/interactivate/activities/koch/what.html

What is the Koch's Snowflake Activity? This activity allows the user to step through the generation of a fractal made from deforming a line by bending it. This activity allows the user to step through the generation of a fractal made from deforming a line by bending it. The Koch Curve was studied by Helge von Koch in 1904. When considered in its snowflake form (see below) the curve is infinitely long but surrounds finite area. To build the original Koch curve, start with a line segment 1 unit long. (Iteration 0, or the initiator) Replace each line segment with the following generator: Note that we are really taking the original line segment and replacing it with four new segments, each 1/3 the length of the original. Repeat this process on all line segments. Stages 0, 1 and 2 are shown below. The limit curve of this process is the Koch curve. It has infinite length. Notice also that another feature that results from the iterative process it that of self-similarity, i.e., if we magnify or "zoom in on" part of the Koch curve, we see copies of itself. The idea of the Koch curve was extended to the Koch "Snowflake" by applying the same generator to all three sides of an equilateral triangle; below are the first 4 iterations.

76. TPE Fractales : Le Flocon De Von Koch http://irchat.free.fr/tpefractales/vonkoch.php

@import url("style.css"); BOURDEAUDUCQ Sébastien / RIQUET Jean Charles TPE Fractales Vous êtes ici : Version imprimable Sommaire Page d'accueil et introduction I - Présentation Définition d'une fractale Le flocon de Von Koch Le triangle de Sierpinski L'ensemble de Mandelbrot Autres fractales basées sur les complexes La dimension fractale II - Les fractales dans la nature 1. Etude d'objets fractals naturels La côte de Bretagne Chez les végétaux : Le chou-fleur Le chou romanesco Les fougères Dans le corps humain : L'intestin grêle Les poumons Le réseau coronarien 2. La modélisation des fractales naturelles Les L-systèmes IFS Conclusion Divers Biographies des personnes célèbres ayant étudié les fractales Benoît Mandelbrot Gastion Julia Waclaw Sierpinski Helge Von Koch Michael Barnsley Annexes Bibliographie Le TPE Nous contacter Livre d'or E-mail Le flocon de Von Koch D'après la définition, la méthode la plus simple pour obtenir une courbe fractale va être de partir d'une figure géométrique (appellée l' initiateur ) puis de remplacer une de ses parties par une autre figure, le

77. Koch Snowflake -- From MathWorld A fractal, also known as the koch island, which was first described byHelge von koch in 1904. It is built by starting with an equilateral http://mathworld.wolfram.com/KochSnowflake.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Applied Mathematics Complex Systems Fractals Koch Snowflake A fractal , also known as the Koch island , which was first described by Helge von Koch in 1904. It is built by starting with an equilateral triangle , removing the inner third of each side, building another equilateral triangle at the location where the side was removed, and then repeating the process indefinitely. The Koch snowflake can be simply encoded as a Lindenmayer system with initial string string rewriting rule Let be the number of sides, be the length of a single side, be the length of the perimeter , and the snowflake's area after the n th iteration. Further, denote the area of the initial n triangle and the length of an initial n = side 1. Then The capacity dimension is then Now compute the area explicitly

78. Koch-Kurve | Mathe Board Lexikon Translate this page koch-Kurve. Die koch-Kurve ist eine vom schwedischen MathematikerHelge von koch erstmals 1904 vorgestellte Kurve. Es handelt sich http://www.matheboard.de/lexikon/index.php/Koch-Kurve

Startseite Mathe Board Lexikon Mathe Tools ... Partner Das Mathe Board: Kostenlose Nachhilfe in Mathematik von der Grundschule bis zur Hochschule. A B C D ... Z Koch-Kurve Definition, Erklärung, Bedeutung Verbessern Mitmachen Koch-Kurve Die Koch-Kurve ist eine vom schwedischen Mathematik er Helge von Koch erstmals vorgestellte Kurve . Es handelt sich bei ihr um eines der ersten formal beschriebenen fraktalen Objekte. Die Koch-Kurve ist auch als Kochsche Schneeflocke bekannt; letztere entsteht aus geeigneter Kombination dreier Koch-Kurven. Inhaltsverzeichnis showTocToggle("Anzeigen","Verbergen") 1 Konstruktion 1.1 Konstruktion Graphisch dargestellt 2 Eigenschaften 3 Kochsche Schneeflocke ... 6 Weblinks Konstruktion Man kann die Kurve anschaulich mittels eines iterativen Prozesses konstruieren. Zu Anfang ist ein Linienstück der Länge "1" gegeben. Die Iteration besteht nun darin, dass alle Linienstücke der Kurve in drei gleichlange Stücke unterteilt werden, auf dem jeweils mittleren Stück ein gleichseitiges Dreieck errichtet wird, und

79. Methode Koch Translate this page Baumwert- und Baumschadenberechnung - Grundsätze der Methode koch -. HelgeBreloer. Die Wertermittlung von Bäumen und Sträuchern als Schutz- und http://www.methodekoch.de/ziffer05.htm

Baumwert- und Baumschadenberechnung Helge Breloer * Der BGH zur Naturalrestitution im Kastanienbaumurteil vom 13.5.1975:

80. Flocon De Von Koch. continue sans tangente, obtenue par une construction géométrique http://www.chez.com/algor/math/koch.htm

Flocon de von Koch. En 1904, Helge von Koch (1870-1924 - Suède) publie l'article : « Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire » qui décrit la ligne actuellement connue sous le nom de 'flocon de von Koch'. La méthode. Pour tracer cette courbe, il faut: Tracez un triangle équilatéral Remplacer le tiers central de chaque côté par une pointe dont la longueur de chaque côté égale aussi au tiers du côté Recommencer cette construction sur chaque côté des triangles ainsi formés. Un peu d'aide. Reprenons la construction de la première étape: Si on considère que les points a et b ont pour coordonnées (x a ,y a ) et (x b ,y b ), nous obtenons: le point c (fin du premier tiers de ab) a pour coordonnées: (x a +(x b -x a )/3, y a +(y b -y a le point d (fin du deuxième tiers de ab) a pour coordonnées: (x a +2*(x b -x a )/3, y a +2*(y b -y a le point e (sommet du triangle construit sur le tiers central de ab) a pour coordonnées: ((x c +x d )*cos 60°-(y d -y c )*sin 60°, (y c +y d )*cos 60°+(x d -x c )*sin 60°) Comment faire?

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